Building construction



June 29, 1954 R. B. FULLER BUILDING CONSTRUCTION 6 Sheets-Sheet 1 FiledDec. 12, 1951 m we NTOR RICHARD BUCKMINSTER FULLER av ATTORNEY June 29,1954 R. B. FULLER 2,682,235

1 V NTOR. RICHARD BULKMINSTER FULLER ATTORNEY June 29, 1954 R, FULLER2,682,235

BUILDING CONSTRUCTION Filed Dec. 12, 1951 6 Sheets-Sheet 3 '1 1 1 g f IlI Q A i INVENTOR.

Ric/m0 BumM/Nsm? FULLER Z7 ydvawz/a A TTORNE Y June 29, 1954 z/gfINVENTO RICHARD BULKMINSTER FULLER ATTORNEY June 29, 1954 R. B. FULLER 3BUILDING CONSTRUCTION Filed Dec. 12, 1951 6 Sheets-Sheet 5 a o--t-:-w:-o0 J/ j 49 4y z INVENTOR. RICHARD Bucmmsrsn FULL ER ATTORNEY June 29,1954 R. B. FULLER BUILDING CONSTRUCTION 6 Shee ts-Sheet 6 Filed Dec. 12,1951 m m m RICHARD BUCKM/NSTER FULLER W ATTORNEY Patented June 29, 1954UNITED STATES PATENT OFFICE 13 Claims.

My invention relates to a framework for enclosing space.

SUMMARY A good index to the performance of any building frame is thestructural weight required to shelter a square foot of fioor from theweather. In conventional wall and roof designs the figure is often 50lbs. to the sq. ft. I have discovered how to do the job at around 0.78lb. per sq. ft. by constructing a frame of generally spherical form inwhich the main structural elements are interconnected in a geodesicpattern of approximate great circle arcs intersecting to form athree-way grid, and covering or lining this frame with a skin of plasticmaterial.

My three-way grid of structural members results in substantially uniformstressing of all members, and the framework itself acts almost as amembrane in absorbing and distributing loads. The resultant structure isa spidery framework of many light pieces, such as aluminum rods, tubes,sheets, or extruded sections, which so complement one another in theparticular pattern of the finished assembly as to give an extremelyfavorable weight-strength ratio, and withstand high stresses. Forexample, the 8C270 Weatherbreak constructed in accordance with myinvention will support 7 lbs. with each ounce of structure and is ableto withstand wind velocities up to 150 miles per hour. It is a dome 49ft. in diameter, enclosing 20,815 cu. ft. of space, yet the frame ismade of light short struts which pack into a bundle 2 ft. by 4 ft. by 5ft., weighing only 1000 lbs. The plastic skin weighs 140 lbs., makingthe total weight of this weatherbreak a mere 1140 lbs.

Definitions of terms The basic and fundamental character of theinventive concept herein disclosed makes it desirable to definecarefully certain terms some of which are used with special connotation,as follows:

Geodesic-Of or pertaining to great circles of a sphere, or of arcs ofsuch circles; as a geodesic line, hence a line which is a great circleor arc thereof; and as a geodesic pattern, hence a pattern created bythe intersections of great circle lines or arcs, or their chords.

Spherical-Having the form of a sphere; includes bodies having the formof a portion of a sphere; also includes polygonal bodies whose sides areso numerous that they appear to be substantially spherical.

Icosahedron.-A polyhedron of twenty faces.

Spherical icosahedron.An icosahedron exploded onto the surface of asphere; bears the same relation to an icosahedron as a sphericaltriangle bears to a plane triangle; the sides of the faces of thespherical icosahedron are all geodesic lines.

Icosacap.-Five spherical triangles of a spherical icosahedron, having acommon vertex.

Grid.A pattern of intersecting members, lines or axes; usuallyintersecting great circles forming patterns made up of equilateraltriangles, diamonds or hexagons.

EquiZateraL-Having all the sides approximately equal. The extent ofvariation in length of sides is determined trigonometrically orempirically by constructing three-way grids on the modularly-dividededges of the faces of a spherical icosahedron.

Modularly divided.Divided into modules, or units, of substantially equallength.

Framework.-The frame of a structure for enclosing space; may beskeletal, as when made of interconnected struts; or continuous, as whenmade of interlocking or interconnected sheets or plates.

The meanings of these and other terms used in describing the inventionwill be more fully comprehended when considered with reference to theaccompanying drawings and diagrams and the explanation thereof.

In its general arrangement, my building framework is one of generallyspherical form in which the longitudinal centerlines of the mainstructural elements lie substantially in great circle planes whoseintersections with a common sphere form grids comprising substantiallyequilateral spherical triangles. The visible pattern formed by thestructural elements themselves does not necessarily show grids ofequilateral triangles, for the visible grids may be equilateraltriangles, equilateral diamonds or equilateral hexagons, the diamondsbeing made up of two equilateral triangles and the hexagons being madeup of six equilateral triangles. The individual triangles, diamonds orhexagons as the case may be, may be made of straight or flat elements,in which circumstance they define flat or plane figures; or they may bemade of arcuate or spherical form to define spherical figures. Eitherway, the complete structure will be spherical, or substantially so. Andeither way, the individual structural elements are so arranged as to bealigned with great circles of a common sphere.

In my preferred construction, the grids are formed on the faces of aspherical icosahedron.

Each of the twenty equal spherical equilateral triangles which form thefaces of this construction is modularly divided along its edges. Linesconnecting these modularly divided edges in a three-way great circlegrid provide the out-v line for the plan of construction. I have foundthat if the structural members be aligned with the lines of the grids,the resulting framework will be characterized by more uniform stressingof the individual members than is possible with any constructionheretofore known. The structural members may be aligned with all linesof the three-way grid, or just with selected ones of those lines. If themembers are arcuate, or spherical, they will coincide with the gridlines; if they are straight, or fiat, they will be chords of the greatcircles which are the grid lines.

A further general aspect of my preferred construction which may be notedhere is that there is a six-ness throughout the pattern of structuralelements on each face of the spherical icosahedron except that at eachvertex, where five faces join at the center of an icosacap, there is afive-ness. In the case of. a skeletal framework made up of struts in apattern of equilateral triangles, this six-ness is manifested by thefact that there are six such triangles around every vertex except at thevertexes of the icosacaps where the five-ness is manifested by the factthat there are only five such triangles around those vertexes.Similarly, in the case of a continuous framework made up ofdiamond-shaped sheets, we find a five-ness only at the vertexes of theicosacaps where five sheets toe in to the one point. This aspect offive-ness and six-ness will be described more in detail further on, andneed be mentioned only in general terms here so as to lay a foundationfor the description of various specific frameworks built according tothe invention.

DESCRIPTION In the drawings:

Fig. l is an elevational View of a building framework constructed inaccordance with my invention and exemplifying a preferred form thereof;and Fig. 2 is a top plan view of the same framework. These views arenecessarily somewhat schematic because of the limitations imposed by thesmallness of the scale to which they are drawn, making it impossible toshow the detail of individual struts or of the fastenings which holdthem together.

Fig. 3 is a diagrammatic perspective view of an icosahedron; and Fig. 4a view of the same icosahedron after it has been exploded onto thesurface of a sphere. These views are included to explain the structuralbasis of the main outlines of the framework of Figs. 1 and 2'.

Fig. 5 is a detail plan view of a portion of the framework of Figs. 1and 2, being that portion which immediately surrounds the top centralvertex, i. e. the central part of the icosacap seen in Fig. 2.

Fig. 6 is a vertical section on the line 68 of Fig. 5.

Figs. 7 and 8 are detail views of my preferred form of strut fastening.Fig. '7 is a central vertical cross-sectional view through the fasteningwith two struts fixed therein, one of these being shown in centralsection and the other in elevation. Fig. 8 is a horizontal sectionalview taken as indicated at 3-43 in Fig. 7, one of the struts being shownin elevation.

Fig. 9 is a detail sectional view taken on the line 99 of Fig. '7.

Fig, 10 is a diagrammatic plan view of a modified construction in whichthe vertexes of the pentagons and adjoining hexagons are offset inwardlyto form an involuted truss-like structure. This view represents aportion of the framework similar to that shown in Fig. 5. However,instead of showing the framework itself, the planes of the equilateraltriangles formed by the struts of the framework are shown as though theywere triangular panels so as to permit shading of the view in such a wayas to pictorialize the resulting dimpled surface.

Fig. 11 is a diagrammatic cross-sectional view taken on the line ll-ilof Fig. 10.

Fig. 12 is a diagrammatic cross-sectional view similar to Fig. 11showing a further modification in which the vertexes of the pentagonsand adjoining hexagons are offset outwardly to form an involutedtruss-like structure which is the inside-out of the structure of Fig.11.

Fig. 13 is a fragmentary plan view of another embodiment of theinvention, and Fig. 14 is a transverse sectional view of the same, takenas indicated at I 4l4 in Fig. 13. Figs. 13a and 1322 are detailperspective views of certain component parts of the truss illustrated inFigs. 13 and 14.

Fig. 15 is a diagrammatic plan view illustrating a portion of aframework in which the main.

structural elements consist of interconnected sheets.

Fig. 16 is a detail plan view of one of the sheets used in the frameworkof Fig. 15 and Fig. 17

' is a detail longitudinal sectional view of such a sheet taken asindicated at lii'i in Fig. 16.

Fig. 18 is a further detail view of the Fig. 15 framework showing themanner in which four adjacent sheets are interconnected or interlocked.

The framework construction illustrated in Figs. 1 to 9 inclusive isrepresentative of the best mode devised by me of carrying out myinvention particularly as utilized in structures up to approximately 50feet in diameter. The struts which comprise the structural elements ofthis framework form a portion of a spherical icosahedron 2?) whosemodularly divided edges 2i are interconnected by three-way great circlegrids 22. A spherical icosahedron has been defined above as anicosahedron exploded onto the surface of a sphere. This definition willbe further explained by reference to Figs. 3 and 4, Fig. 3 being adiagrammatic perspective view of an icosahedron, and Fig. 4 a view ofthe same icosahedron exploded or projected onto the surface of a sphere.The icosahedron has twenty equal equilateral triangular faces. Thespherical icosahedron has twenty equal equilateral spherical triangularfaces. As used here, the term face refers to an imaginary sphericalsurface bounded by the sides or edges of one of the twenty sphericaltriangles.

The edges of each spherical triangle are modularly divided and areinterconnected by the three-way great circle grids 22 previouslymentioned. These grids are formed of a series of struts each of whichconstitutes one side of one of the substantially equilateral trianglesdefined by the lines of the grid. Each strut 23 is aligned with a greatcircle of the sperical icosahedron. Otherwise stated, the longitudinalcenterline of each strut, or main structural element 23, liessubstantially in a great circle plane. In the complete framework, thelongitudinal centerlines of the main structural elements 23 liesubstantially in great circle planes whose intersections with a commonsphere form grids 22 comprising substantially equilateral triangles.

The number of modules into which each edge of the spherical iscosahedronis divided is largely a matter of choice. In the framework of Figs. 1,2, 5 and 6, the number is 16. Therefore we say the frequency is 16. Butit might be 8 or 4 or some other number. Generally speaking, the largerthe structure the greater will be the frequency selected in order tokeep the sizes of individual struts within. practicable limits for easeof manufacture, storage, packing, shipment, handling and erection. Iprefer to use light metal pieces for the struts, e. g. aluminum tubes asshown in Figs. '7 and 8. One metal alloy presently considered mostsuitable is the alumi num alloy known generally under the designation61ST. A tubular strut size found satisfactory for structures 40 ft. indiameter is approximately 4 ft. long by 1 outside diameter by 0.032 wallthickness. In general, I prefer to use struts which have a ratio of 24units in length to 1 unit in transverse dimension, 1. e. the slendernessratio is 24 to 1. The frequency of the pattern as above defined can beselected with view to maintaining the optimum slenderness ratio for eachsize of framework.

The struts 23 may be interconnected by sliding joints locked by gravitycompression acting throughout the great circle pattern of the frameworkas a whole. In erecting the framework it is best to start by assemblingthe struts which are to form the very top of the dome, i. e. at thecenter of the icosacap seen in Fig, 2. can be done on the ground.Working radially outward in all directions, the dome will begin to takeform and will gradually be lifted as the work proceeds until in the endits rest with its lowermost struts against the ground or on a suitablefoundation prepared to receive it. It may be locked to the foundation bygreat circle bands or cables preferably extending along the great circlelines which define the edges of the icosahedron. If a poured concretefoundation is used, the lowermost struts and fastenings, or the ends ofsuch struts, may be embedded in the foundation, in which case theconcrete, or portions thereof, is poured after erection of the frameworkhas been completed. Alternatively, the lowermost struts and/or thefastenings may be anchored to individual concrete foundation posts or toeye-bolts or other fastenings in such posts. In this arrangement anysuitable auxiliary fastenings may be used to lock the framework to thefoundation fastenings, such as bolts, cables, turnbuckle rods, etc.,this being largely a matter of choice depending upon the type ofconstruction best suited for a particular purpose.

Referring again particularly to Figs. 1 and 2, the ground line orfoundation line is indicated at A-A in Fig. 1, and the components of theframework are so oriented that the midpoint of the pentagon at thecenter of an icosacap coincides with the zenith Z of the framework. Insome cases, however, it may be preferred to shift the orientation of theframework, as for example to an orientation which would result fromusing the line A'A' as the ground or foundation line, in which case thezenith Z would no longer coincide with the midpoint of an icosacap butinstead would coincide with a point within one of the sphericaltriangles which form the faces of the icosahedron. If the sheet of thedrawing on which Fig. 1 appears be turned so that its righthand longeredge becomes the bottom of the This sheet, that part of Fig. 1 which isbounded by ZAA', becomes the right-hand portion of the reorientedframework. Note that with this particular orientation, the base line A'Ais a geodesic line completely defined by struts of the framework. Thisprovides a convenient foundation line and one which lends itself well toanchoring of the framework to its foundation. In Figs. 1 and 2, however,I have chosen the zenith Z orientation in order to provide a clearillustration in Fig. 2 of a complete icosacap as defined hereinabove.

One of the characteristics of the completed framework is that it isvirtually self-locking. Once properly assembled in the manner described,it will not come apart except by more or less uniform expansion of allits parts. However, because the framework is somewhat resilient,localized forces acting outwardly against the inside Of the structuremay under certain conditions tend to expand one portion of the frameworkand produce what might be described as somethin akin to a blowout in apneumatic tire. To resist such forces, and to assist in holding thestruts together during erection, it is best that the mean for fasteningthe ends of the struts be such as to lock them positively in place, inthis respect supplementing the self-locking action described above, andgiving added strength to the framework by reason of the fixed-endconstruction thus provided.

My preferred form of fastening is shown in Figs. '7-9. It is a ball-likefist configuration designated generally at 24, comprising complementaryparts 25 and 21. In the specific construction illustrated, 25 is theouter part and 2'! the inner part. These parts are clamped together bymeans of a bolt 28, a coil spring 29 being provided to afford a certainamount of resiliency in the fastening, which is particularly usefulduring erection of the structure. As seen in Fig. 7, outer part 25 is inthe general form of an inverted bell, the edge of which is turned backon itself to provide a curved flange 26 complementary to the curvedflange of inner part 21. Affixed to each end of each strut 23 is anattaching member as having a tubular body portion 45, the shouldered endto of which fits within the end of the strut. Attaching member 30 may besecured to the strut 23 by means of a rivet, pin or bolt 3|. Eachfastening member has an inwardly extending lug 32 and an outwardlyextending lug 35. Lug 32 has a pair of flanges 34 with arcuate edgesconforming to the arc of the inner surface of inner part 27 of thefastener. Similarly lug 35 has a pair of flanges 35 whose arcuate edgesconform to the inner surface of flange 26 of outer part 25. A pair offlanges 33 at the end of fastening 35 have arcuate edges conforming tothe outer surface of the bell-like por tion of outer fastening 25. Thearrangement is such that the longitudinal centerline of struts meetingat any particular fastening 2 3, 2'! can be adjusted to different anglesso that the struts will form chords of great circles of the framework asa whole. As the framework is erected, it will tend to assume the generalspherical form of the dome for which parts have been designed. Once ithas assumed such form, the individual fastenings are tightened,compressing the coil springs 29 to the desired extent. If the fasteningsare tightened to the extent which compresses springs 29 until they aredriven solid, maximum rigidity is obtained. However, if greaterflexibility is desired in the completed structure, bolts 28 will betightened to a lesser extent, in which case the springs 29 will not bedriven solid. Suitable lock nuts or lock washers may be used to hold theparts in the desired final adjustment.

In Fig. 7, bolt 28 is provided with an eye 31 at its inner end which isuseful in attaching the plastic skin inside of the framework. Bolt 28passes through openings 38, 39 in the outer and inner parts 25, 21respectively of fastening 24.

Reference is now made to the modified construction illustrated in Figs.10 and 11. Fig. represents a portion of the framework similar to thatshown in Fig. 5. However, instead of showing the framework itself, theplanes of the equilateral triangles formed by the struts of theframework are shown as though they were triangular planels (instead ofspaces outlined by the struts). This has been done to permit use ofshading in such a way as to pictorialize the dimpled surfaces of thisparticular framework. The dimples are formed by inwardly offsetting thevertexes of the pentagon AD and adjoining hexagon M to form what I terman involuted truss-like structure. This places all the inwardly offsetvertexes substantially in a spherical surface 42 concentric with themain spherical surface 43. The main spherical surface is defined by theends of the struts of the bases of the pentagons 4t and hexagons ll. Theresulting structure is like a spherical truss defining inner and outersubstantially spherical surfaces of concentric sphere-s. This frameworkbased on two spheres is somewhat stiffer and less resilient than theframework of Figs. 1 and 2 based on a single sphere, and I consider theformer best suited for the construction of domes in sizes rangingbetween approximately 50 and 140 feet in diameter. The struts whichextend inwardly to the vertexes or points of the dimples are madesomewhat longer than they would be in the single sphere construction sothat, upon assembly, formation of the dimples is an inherent function ofthe lengths of the respective struts.

In the further modification illustrated by Fig. 12', the dimples areinverted. This framework, and the framework of Figs. 10 and 11, can bemade of the same kind of struts described with reference to Figs. 5 and6, and can be put together with the same type of fastening describedwith reference to Figs. 7 and 8, although if desired other forms ofstruts and fastenings can be used within the limits of the appendedclaims. It will be observed that the fastenings of Figs. 7 and 8 allowfor offsetting of the selected vertexes. (Note the clearance at 14.)Note also that in these modified constructions the struts which extendto the offset vertexes, while no longer lying substantially in aspherical surface, still are aligned with great circles of a commonsphere; and such struts still lie substantially in great circle planeswhose intersections with a common sphere form grids comprisingequilateral triangles. These inwardly extending struts also are chordsof great circles of the framework.

Reference is now made to another embodiment of the invention asillustrated in Figs. 13 and 14. This is a variant of the frameworks ofFigs. 10-12; like them, it is based on two spheres. However, theframework of Figs. 13 and 14 is more complex, and comprises a trussformed of compres sion and tension members. I consider this type offramework best suited for the construction of domes in sizes fromapproximately 1 10' feet in diameter and upwards. Fig. 13 covers a smallarea of the framework centering about the penthe light and dark tripods.

tagon at the midpoint of an icosacap, he an area corresponding to thecentral portion of Fig. 5 (except, of course, that this is a different.type of framework than that shown in Fig. 5). The framework is made upof struts similar to the struts 23 described with reference to theframework of Figs. 1, 2, 5 and 6, these struts being connected togetherby fastenings which may be similar to those described with reference toFigs. 7-9. The framework may be considered as made up of a series oftripods, one of which is shown in, Fig. 13a, consisting of three struts41 joined at the center of the tripod by fastening 48. This particulartripod may be described as an outwardly pointing tripod. Its centralvertex as represented by fastening 48 lies in the main, or outer,spherical surface 5| and its base lies in spherical surface 52concentric with surface 5|. Arranged in complementary fashion to theroutwardly pointing tripods are inwardly pointing,

tripods made up of three struts 49 joined together by fastening 58. Itscentral vertex as represented by fastening 5B lies in the innerspherical surface 52 and its base lies in the outer spherical surface5|. Two such complementary tripods are shown in Fig. 13b. The feet ofthe outwardly pointing tripods are joined together by tension members 53which may be made of wires or cables. The feet of the inwardly pointingtripods are connected by similar tension members 54.

In Figs 13 and 14, the struts 47 of all of the outwardly pointingtripods have been shown without any surface shading so that they appearlight in the drawing, whereas-the struts 49 of all the inwardly pointingtripods have been shown with surface shading so that they appear dark inthe drawing. Thus, the light tripods are disposed with their vertexes inspherical surface 5! and the dark are disposed with their vertexes inspherical surface 52'. Tension members 55 extend diagonally between therespective feet of These: tension members, as viewed in plan in Fig. 13,presenta hexagonal outline, alternate corners of which are connected bythe aforesaid tension members 53 and 54, tension members 53 forming atriangle made up of chords of spherical surface 52 and tension members54 forming a triangle made up of chords of spherical surface St. Theresultant basic pattern of the outer spherical icosahedron in surface 5|is the same as that illustrated in Fig. 5'. The same is true withrespect to the resultant basic pattern of the inner sphericalicosahedron in surface 52. In effect, therefore, we have here twoconcentric spherical icosahedrons joined by diagonal struts and tensionmembers. The framework is tightened into a final rigid structure bymeans of tension members 58- extending radially with respect tosphericalsurfaces 51 and 52 between the fasteni'ngs 48 and 50 at theapexes of the light and dark tripods respectively. If desired,turnbuckles may be used in these tension members to secure the desiredfinal tension to hold the structure with the proper degree of rigidity.

At the vertexes of the icosacap, the framework assumes a pentagonal formas clearly shown at the center of Fig. 13. At such points in the structure wehave an inwardly (or outwardly) pointing pentagonal strutarrangement in place of the two complementary tripods which characterize the rest of the framework where the pattern is hexagonal. I preferto bridge over the outer side, or base, of. the pentagonal strutarrangement at each vertex. In the specific framework. shown,

this bridging consists of five struts 57 joined together by fastenings58 at the vertexes of the spherical icosahedron, and joined byfastenings 59 to the feet of the light and dark tripods immediatelyadjoining the respective pentagons.

In all of the forms of framework I have described, the lengths of theindividual struts are substantially equal, but not precisely so. Theslight differences in the lengths of different struts in a givenframework determine the radius of the dome and whether it is based onone or two spheres. The number of different lengths of strut in anygiven framework based on spherical icosahedron varies in accordance withthe number of units, or modules. into which the edges of the sphericalicosahedron are divided, i. e. in accordance with what I have previouslytermed the frequency of the three-way great circle grids. I have foundthat with a frequency of 16, as described in connecii'm with the domeillustrated in Figs. 1, 2, and 6, all conditions of the framework designare satisfied with 56 different lengths of strut. The same frameworkwhen built of grids having a frequency of 8 can be constructed fromstruts in 16 different lengths. With a frequency of i, only 5 differentlengths would be used. I have found, further, that there need never beany greater complication as to number of lengths of struts than thatrepresented by a frequency of 16.

The slight differences between the lengths of the individual struts inturn create slight differences between the angles of the substantiallyequilateral triangles and this has the result of forming a sphericalgrid structure in which all the main structural members are in geodesicalignment or are chords of great circles of a common sphere. One way ofdetermining the strut lengths is to construct a paperboard hemisphere toa scale of, say, 1 inch to 1 foot, and lay out the vertexes of one ofthe faces of a spherical icosahedron on its surface. These vertexes arenext connected by drawing great circle lines (spherical straight lines)therebetween. The edges of the triangle defined by these lines are nextdivided equally into the number of units represented by the selectedgrid frequency. The division points are then connected by drawing greatcircle lines in the manner clearly shown in Figs. 1 and 2. (Note thatthe points along one edge are connected to every second point on an--other edge.) We now have a completed threeway grid pattern. Finally thelength of the chordal struts is measured directly with the use ofordinary draftsmans dividers, allowance being made for the strutfastenings.

Figs. to 18 inclusive illustrate another embodiment of my invention inwhich the main structural elements of the framework consist ofinterconnected sheets 50 of metal, plastic or other suitable material.The longitudinal centerlines ll-|1. Fig. 16) of these sheets liesubstantially in great circle planes whose intersections with a commonsphere form grids comprising substantially equilateral triangles. Asshown the sheets are substantially in the form of equilateral diamondswhose minor axes are approximately equal in length to the sides. Thecorners of the sheets 60 are notched for interlocking engagement withthe notches of adjacent sheets. The corners of the notches ii! and [i2lie substantially in great circle planes whose intersections with acommon sphere form grids of substantially equilateral sphericaltriangles. Thus the sheets 60, like the struts 23 of the frameworkillustrated in Figs. 1

and 2, are in geodesic alignment. The alignment is such that thelongitudinal centerlines of the sheets (and also their edges) arearranged in geodesic lines. Thus these sheets create the same sort ofthree-way grid pattern as I have described with reference to the severalforms of framework in which struts are employed.

Here again, all the main structural elements are of almost the samesize, the variation being determinable mathematically or by graphicsolution as before. The frequency of the grids is a matter for selectionin accordance with the special requirements of particular structures. Aswith the struts, the frequency will determine the number of differentdiamond sizes to be used in a given framework design. With a frequencyof 16, for example, there will be 20 sizes or types of diamond persphere. With hexagonal sheets on the same three-way grids, and with afrequency of 16, there will be 10 types per sphere, consisting of 9types of approximately hexagonal sheets and 1 pentagonal sheet. Otherforms and arrangements are possible.

Particular attention is directed to the manner in which the three-waygrid pattern is built up in this form of my framework. Fig. 15 shows onecomplete face, or spherical triangle EST, of the spherical icosahedron,plus one-third of each adjoining face of the same, namely the additionalareas RUS, SVT and TWR, or the total area RAUSVTW. Geodesic lines 63,63, 63 extend from each vertex of RST through the mid-point of theopposite side. SV, VT, TW, etc. are corresponding geodesic lines of theadjoining faces of the spherical icosahedron. Within area RUSO all ofthe sheets 60 are arranged with their longitudinal centerlines extendingin one general direction. The same is true within areas SVTO and TWRO,except that in each case the general direction is diiferent. Along linesR0, SO and TO, the sheets of the respective adjoining areas cometogether at an angle approximately equal to one of the spherical anglesof spherical triangle RST. This can best be understood by noting thediamond patterns of the construction lines where they extend beyond thearea covered by the sheets 60. Note that at the vertexes of theicosacaps (as at S for example), five sheets 6| toe in to a com monpoint. Elsewhere throughout the framework as shown in Fig. 18 foursheets toe in to a common point, except at the center 0 of the triangleRST where only three sheets toe in at a common point. Thus there arefive sheets around each of the vertexes R, S and T, three sheets aroundcenters 0, U, V and W and four sheets around all intermediate points.

With this general type of construtcion, I have discovered thepossibility of making all the sheets exactly identical in overall size,the variation in type being secured by varying the sizes or depths ofthe notches BI and 62. If the overlapping edges of adjacent sheets areriveted together, the holes for the rivets will be drilled on slightlydifferent patterns to suit the different types and keep the fasteningsin geodesic alignment. Thus all the sheets are sheared out to one size,and. the manufacture of the different types for a particular sphere iscompleted by using adjustable jigs (or a series of difierent jigs) forthe notching and/or drilling or punching tools. This greatly simplifiesmanufacture.

I prefer to form or press the sheets to a compound curvature conformingto the surface of the spherical icosahedron on which they are based.

Domes constructed in accordance with Figs. 15-18 may be erected by firstassembling on the ground those sheets which are at the vertex of anicosacap, namely at that vertex which W111 be uppermost in the completedframework. Then, working around peripherally, additional sheets areinterlocked. and/or riveted together, raising the partially completeddome as the work progresses.

It is possible to begin interlocking the sheets in either a clockwiseoverlapping relationship, or in a counterclockwise overlappingrelationship. By a clockwise overlapping relationship, I mean that atany given point where a group of sheets toe in to a common vertex, theedge of each successive sheet of the group is on top of the precedingsheet as we move around the vertex in a clockwise direction. By acounterclockwise overlapping relationship, I mean that at any givenpoint where a group of sheets toe in to a common vertex, the edge ofeach successive sheet of the group is on top of the preceding sheet aswe move around in a counterclockwise direction. This imposes what I terma turbining action in the framework, and the turbining action will beeither clockwise or counterclockwise according as the overlappingrelationship is either clockwise or counterclockwise. These turbiningactions produce a highly effective locking action in the framework as awhole.

Geodesic locking bands or cables may be tensioned over the completeddome and anchored to a suitable foundation.

Geodesic frameworks constructed in accordance with my invention, if madeof struts uni- Versally jointed at the vertexes of the triangles can befolded into a compact bundle without taking apart any but the finallocking elements. This form of my invention is ideally suited for use astemporary shelters which are to be moved from place to place, such ashuts, hangars, messhalls, and headquarters units for army encampments.

The frameworks may be covered with plastic skins, inside or outside orboth, or with other materials. Openings for access, light, sun and airare provided as desired.

The terms and expressions which I have employed are used in adescriptive and not a limiting sense, and I have no intention ofexcluding such equivalents of the invention described, or of portionsthereof, as fall within the purview of the claims.

I claim:

1. A building framework of generally spherical form in which the mainstructural elements are interconnected in a geodesic pattern ofapproximate great circle arcs intersecting to form a three-way griddefining substantially equilateral triangles.

2. A building framework of generally spherical form in which the mainstructural elements are arranged in a geodesic pattern of approximategreat circle arcs intersecting to form a threeway grid definingsubstantially equilateral triangles, said main structural elements beinginterconnected by sliding interlocking joints.

3. A building framework of generally spherical 12 form in which the mainstructural elements form a substantially uniform over-all pattern ofgreat circle arcs intersecting in a three-way grid.

4. A building framework of generally spherical form constructed oiintersecting trusses arranged in a geodesic pattern of approximate greatcircle arcs.

5. A building framework of generally spherical form in which the mainstructural elements are aligned with great circles of a common sphere,and are interconnected in a pattern the sides of each element of whichare substantially equal in length.

6. A building framework of generally spherical form in which thelongitudinal centerlines of the main structural elements liesubstantially in great circle planes whose intersections with a commonsphere form grids comprising substantially eqiulateral sphericaltriangles.

'7. A building framework constructed in accordance with claim 6, inwhich the main structural elements are interconnected to form a trussthe outermost points of which lie substantially in a common sphericalsurface.

8. A building framework constructed in accordance with claim 7, in whichthe innermost points of the truss lie substantially in a commonspherical surface within and concentric with the first-named sphericalsurface.

9. A building framework of generally spherical form in which the mainstructural elements consist of interconnected elements the longitudinalcenterlines of which lie substantially in great circle planes whoseintersections with a common sphere form grids comprising substantiallyequi lateral spherical triangles.

10. A building framework constructed in accordance with claim 9 in whichthe meeting edges of the grids form a portion of a sphericalicosahedron.

11. A building framework of generally spherical form in which the mainstructural elements consist of interconnected sheets the longitudinalcenterlines of which lie substantially in great circle planes whoseintersections with a common sphere form grids comprising substantiallyequilateral spherical triangles.

12. A building framework constructed in accordance with claim 11,. inwhich the corners of said sheets are notched for interlocking engagementwith the notches of adjacent sheets.

13. A building framework constructed in accordance with claim 11, inwhich the corners of said sheets are notched for interlocking engagementwith the notches of adjacent sheets and in which the corners of thenotches lie substantially in great circle planes whose intersectionswith a common sphere form grids of substantially equilateral sphericaltriangles.

References Cited in the file of this patent UNITED STATES PATENTS NameDate Pantke Aug. 26, 1930 OTHER REFERENCES Number

